Systems which comply with the IEEE 802.11 standard are commonly referred to as WiFi systems. Many such systems use OFDM (orthogonal frequency division multiplexing) for modulation which divides a frequency band into a number of equally spaced frequency subcarriers (or tones) and data is then modulated onto these subcarriers. The IEEE802.11n standard defines 52 or 56 subcarriers for 20 MHz bands to carry data. Some of these subcarriers (e.g. 4 subcarriers) are not used to carry payload data but instead are used for pilot signals which improve the ability of the coherent detection at a receiver to accommodate frequency offsets and phase noise.
The frame format defined in the IEEE 802.11n standard includes a preamble which comprises short training sequences and long training sequences (or long training fields). The short training sequence is used for AGC (automatic gain control), diversity selection, timing acquisition and coarse frequency acquisition in the receiver. The long training field is used for channel estimation and fine frequency acquisition in the receiver. As these parameters are used to demodulate an OFDM packet, the quality of these initial estimates affects the transmitter modulation accuracy.
A source of errors in such systems, which can impact transmitter modulation accuracy, is quantization. In OFDM, data is modulated onto frequency tones using an IFFT (inverse fast Fourier transform) and the output from the IFFT contains real numbers, i.e. infinite decimal representation. Digital implementations of OFDM output signals using a fixed number of bits i.e. the signals are quantized. The quantized signal is then converted to an analogue signal using a digital to analogue converter. The quantization error which is introduced is the difference between the quantized value and the real number value output from the IFFT. Typically quantization is performed by rounding. There are a number of techniques which can be used to reduce quantization error, such as increasing the number of bits used for quantization or increasing the size of the IFFT (known as oversampling); however these techniques increase the overall cost and complexity of the system.
The embodiments described below are not limited to implementations which solve any or all of the disadvantages of known quantization methods.